Extreme zeros in a sequence of para-orthogonal polynomials and bounds for the support of the measure

In this paper we estimate the location of the extreme zeros (those closest to z=1) of the para-orthogonal polynomials from the (c_n,d_n)-parametrization of the measure, and use this information to establish sufficient conditions for the existence of a gap in the support of \mu at z=1. These results...

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Bibliographic Details
Published in:Mathematics of computation 2018-01, Vol.87 (309), p.261-288
Main Authors: Martínez-Finkelshtein, A., Ranga, A. Sri, Veronese, D. O.
Format: Article
Language:English
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Summary:In this paper we estimate the location of the extreme zeros (those closest to z=1) of the para-orthogonal polynomials from the (c_n,d_n)-parametrization of the measure, and use this information to establish sufficient conditions for the existence of a gap in the support of \mu at z=1. These results are easily reformulated in order to find gaps in the support of \mu at any other z\in \mathbb{T}.
ISSN:0025-5718
1088-6842
DOI:10.1090/mcom/3210